I don’t find your idea as very smart but 1<sup>st</sup> part of your move is right! You have to find niche related blogs and bloggers and you have to contact them, but directly asking them to link back to you didn’t make any sense to me unless you have some great Authority and Value in your Niche.
There are several ways you can get Link to the targeted blogs:
1. Offer them a Guest Posting
Simple but You actually have to write 500+ words of detailed and well researched post just to get a single link or may be 2 pointing it on your website.
2. Run a Contest for Bloggers in your Niche
If your budget is high then offering a competition for bloggers and then through badges and other stuff you can get a link pointing to your website (most badges usually get site wide links)
3. Create Infographics and Email them
Another idea is to create infographics on your site and email them the update about it. If the piece of graphic will be informative and well designed, chances are that they will link back to you!
4. Interviews
Try and target influencers in your niche and Interview them and post it on your own blog. As they are influencers so chances are that you will get lots of natural links to your site (depending upon the fame of the influencer and blog itself!)
These are just few of the ideas! Link Building is way too big and the only boundary to link building is your own personal imagination!